Conservation of Energy:
q – w = h + pe + ke (eq. 1)
By making the assumptions presented previously, eq. 1 can be reduced to
h = 0 or h1 = h2 (eq. 2)
It is more useful to expand eq. 2:
u1 + P1v1 = u2 + P2v2 (eq. 3)
where
P is the pressure
u is the internal energy, and
v is the specific volume.
Quality
x = mvapor (eq. 4)
mtotal
where mvapor is the mass of the vapor, and
mtotal is the total mass of the liquid and the vapor
It can be derived that:
x = (hav – hf)/hfg (eq. 5a)
x(exit) = (h(e) – hf(e) )/hfg(e) (eq. 5b)
where hf is the specific enthalpy of the liquid
hfg is the difference between the specific enthalpy of the fluid and the gas, and
hav is defined as hf + xhfg.
the subscript e is for the exit pressure
Procedure:
Measure the temperature and pressure at the inlet (1) and exit (2) of the throttling
valve. NOTE: The numbers (1) and (2) do not correspond to the sensor numbers, but
they do correspond to the numbers in figure 1.
2. Measure the mass flow rate of refrigerant (read from indicator on the sensor).
3. Repeat step 1 for at least 2 more settings on the air conditioner (e.g. low, med, high).
Analysis:
Questions 1 through 3 need only be evaluated at 1 air conditioner setting.
Using only the inlet pressure reading and assuming that the refrigerant is a saturated liquid as it flows through the throttling valve, find the specific enthalpy.
Assuming that the enthalpy across a throttling valve does not change, use the enthalpy from question 1 and the reading of the exit pressure, determine what state the mixture at the exit is.
If the refrigerant is a saturated mixture at the exit, find the quality using equation 5b.
Using the temperature and the pressure form the inlet reading, does the previous assumption that the inlet and of the throttling valve is a saturated refrigerant? Explain why or why not.
What is the temperature change for this process? A) Using the saturation temperatures from the given pressures. B) Using the data read off of the air conditioner. Is there a difference and if so, explain.
Air Flow Across the Coil
Objective:
To understand the heat transfer principles by determining the convection heat transfer rate involved with cross flow over the coils (tubes).
Background:
There is a coolant flowing inside the coils and as the air flows over the coils, heat is transferred between the flowing coolant in the coil and the air around it. The rate at which the heat is transferred is dependent upon the heat transfer coefficient. The coil rows are either arranged in an aligned or staggered bank.
geometry of the coils
V
, T (Tinlet)
ST
SL
Relevant Equations:
Maximum Velocity of the fluid around the tube
 (eq. 1)
V is the measured velocity
Reynolds number for the air
 (eq. 2)
D is the diameter of the tube
is for the inlet of the air
Air-side Nusselt number
 (eq. 3)
C2, C, and m values come from tables 7.7 and 7.8 from the Heat Transfer book
The other properties are evaluated at the average of the inlet and outlet temperature of the fluid and the subscript s is for the surface temperature.
The average heat transfer coefficient
 (eq. 4)
the k value is from the inlet of the air
Knowing only the inlet temperature of the fluid in the coil
 (eq. 5)
N is the number of coils
NT is the number of coils that are first hit by the air flow
and cp are properties from the inlet of the air
Log mean temperature difference
 (eq. 6)
Ts is the temperature of the coil surface
Heat transfer rate per unit length of the tube
 (eq. 7)
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